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Expressions
Objective: EE.01
I can write and evaluate numerical expressions involving whole number
exponents.
Key Vocabulary:
Fraction: Part of a whole. It has a numerator and denominator. Example: ¾ means 3 out of 4 parts
Decimal: Part of a whole. It has a decimal point. Place value is located to the right of the whole number. Example: 3.45 means 3 and 45 hundredths.Exponent: tells the number, (base), how many times to multiply itself. Example: 3³ = 3 x 3 x 3 = 27Exponents are called powers.
Mathematical Practices:
• MP 2: Reason abstractly and quantitatively.
What does this mean?
I can think about numbers in many ways.
I can take numbers and put them in a real-world context. I can work with numbers mathematically.
Essential Questions:
• 1. What is an exponent? An exponent tells a base how many times to multiply itself.
• 2. How do you calculate a value containing an exponent? You multiply the base the number of times the power indicates.
Exponent Review: Whiteboards
• Write in expanded form:
• 3 -²
• 4 -³
• ½ ³
• 5 0
Bell work Review: Square
• Remember: Area = Length x Width.
• The area for a square is x 2 .
• Find the area of each square:
• A square has a side length of 6 cm.
• A square has a side length of 3 cm.
• A square has a side length of 10 cm.
New Learning!!• Let’s explore different exponents.
• Since we learned that 2 0 equals 1, what do you think 2 -1 will represent? Discuss in your group.
Table: Let’s create a table to learn about negative exponents.
Positive and Negative Exponents
Exponential Expanded Value Rule
2 4 2· 2 · 2 · 2 16 ÷2
2 3 2 · 2 · 2 8
2 2 2 · 2 4
2 1 2 2
2 0 1 1 x2
2 -1 ½ 1 ½ ½
2 -2 ½ 2 ½ · ½ ¼
2 -3 ½ 3 ½ · ½ · ½ 1/8
2 -4 ½ 4 ½ · ½ · ½ · ½
1/16
Note Taking: Exponent Rules
• Any whole number, fraction, or decimal to the power of zero equals 1.
• Any whole number, fraction, or decimal to the power of 1 equal itself.
• Any whole number, fraction, or decimal to the 2nd power makes a square.
Exponent Practice:
• Write the following expressions in exponent form:
• 7 · 7 · 7
• 10 x 10 x 10 x 10 x 10
• 2 · 2 · 2 · 2 · 2
• 3/5 · 3/5 · 3/5
Review!
• 2 0 = ____
• 2 1 = ____
• 2 2 = ____
• 2 3 = ____
1
2
4
8
Exponent Practice:
• Write correctly using exponents:
• (3 + 4) · (3 + 4) +( 4 - 2) · (4 - 2) · (4 - 2)
• (7 + 3) · (7 + 3) - (5 + 1) · (5 + 1)
• (10 – 1) · (10 – 1) ÷ ( 2 + 1) · (2 + 1)
More Exponent Practice:
• Solve the following exponential equation for x:
• X = 3² + 5²
• X = 4³ - 3³
• X = 10² - 7²
• 3. What is a variable? A variable is a letter that represents a number.
• 4. What is Order of Operations? What do the letter PEMDAS represent?
• Order of Operations is a set of rules for solving problems.
• P – Parenthesis
• E- Exponents
• M/D – Multiply or Divide – left to right
• A/S – Add or Subtract – left to right
True or False
4m = m 4
Explain your thinking.
Solve: If m = 3
4m = m + m + m + m or 4 (m)
m4 = m · m · m · m
Group Discussion:
• Look at the following equation:
• 7y = y²
Round Robin: Decide if the equation above is a true or false equation. Explain and defend your group answer.
Key Vocabulary:
• Variable – A variable is a letter or symbol that represents a number (unknown quantity).
• 8 + n = 12
Examples:
• A variable can use any letter of the alphabet.
• n + 5
• x – 7
• w - 25
Properties of and Multiplication
• Get your math book out and turn to page 46.
• Note taking: Properties of Multiplication.
Group Discussion:
• Decide if the following equation is true or false:
• h³ = 3h
• Round Robin: Explain and defend your answer.
Key Vocabulary:
• Algebraic expression – a group of numbers, symbols, and variables that express an operation or a series of operations.
• m + 8• r – 3
Examples:
• Evaluate an algebraic expression – To find the value of an algebraic expression by substituting numbers for variables.
• m + 8 m = 2 2 + 8 = 10• r – 3 r = 5 5 – 3 = 2
Key Vocabulary:
• Simplify – Combine like terms and complete all operations
m = 2
• m + 8 + m 2 m + 8
• (2 x 2) + 8 4 + 8 = 12
Words That Lead to Addition
• Sum
• More than
• Increased
• Plus
• Altogether
Words That Lead to Subtraction
• Decreased
• Less
• Difference
• Minus
• How many more
Let’s Practice: Write Algebraic Expressionsfor These Word Phrases
• Ten more than a number
• A number decrease by 5
• 6 less than a number
• A number increased by 8
• The sum of a number & 9
• 4 more than a number
n + 10
w - 5
x - 6
n + 8n + 9
y + 4
Let’s Practice: Write Algebraic Expressionsfor These Word Phrases
• A number s plus 2
• A number decrease by 1
• 31 less than a number
• A number b increased by 7
• The sum of a number & 6
• 9 more than a number
s + 2
k - 1
x - 31
b + 7n + 6
z + 9
Evaluate each algebraic expression when x = 10
• x + 8
• x + 49
• x + x
• x - x
• x - 7
• 42 - x
1859
20
03
32
Complete This Table
n n - 35
102132
27
1829
Complete This Table
x x + 65
102132
11162738
Let’s Practice: Write an Algebraic Expression for These Situations
• Scott’s brother is 2 years younger than Scott
• The sum of two numbers is 12
• The difference between two numbers is 5
s - 2
v + c = 12
m – n = 5
Review:
http://www.mathsisfun.com/exponent.html
http://www.mathsisfun.com/algebra/index.html
Variables and ExpressionsVariable – a symbol used to represent a quantity that can
change.Coefficient – the number that is multiplied by the variable in
an algebraic expression.Numerical expression – an expression that contains only
numbers and operations.Algebraic expression – an expression that contains
numbers, operations and at least one variable.Constant – a value that does not change.Evaluate – To find the value of a numerical or algebraic
expression.Simplify – perform all possible operations including
combining like terms.
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